The Fibonacci Number Sequence

The Fibonacci Sequence, in mathematics, is a sequence of numbers generated recursively from the two initial term values 1 and 1. The subsequent terms of the sequence can be generated by summing the two previous terms (i.e. for the third term, add 1 and 1 to get 2, for the fourth add 2 and 1 to get 3). This sequence therefore continues to increase forever, and there are an infinite number of Fibonacci Numbers. The sequence was mentioned by Fibonacci around the year 1202 in a book he published, but apparently the sequence had been noticed earlier by Indian mathematicians.

The interesting thing about the Fibonacci Sequence is that it describes all sorts of natural patterns, including the ancestry lines of bees (check out the link for more info about bees and Fibonacci numbers). Now it might be worth noting that these bees, and the other natural objects that seem to array themselves in these patterns, are not conscious of what they are doing and probably couldn’t recreate the list of Fibonacci numbers. It just so happens that this pattern of number recurs without fail in all sorts of scenarios. If you take a piece of graph paper and draw adjacent squares with sizes that correspond to numbers in the Fibonacci Sequence, you would be able to trace out what is called a Fibonacci Spiral, as pictured below:

But wait, it gets better! Try to draw 21 of these spirals in a concentric manner and you’ll get a really cool looking vortex-looking object. Then take the mirror image of the original spiral and draw 13 of the spirals in a concentric manner for another vortex-like object.

Finally, if you super impose these images on top of one another you’ll get a very cool patter that can be identified in nature over and over again:

I chose to use 21 and 13 spirals for my design, however you’ll notice these numbers are neighboring Fibonacci numbers, and yes you can use any two consecutive terms in the Fibonacci sequence and get a similarly beautiful geometric pattern. This spiral pattern can be identified in certain flowering species of plants, pineapples, pine cones, and even cauliflower.